The multivariate bisection algorithm

The aim of this paper is the study of the bisection method in ${\mathbb{R}}^n$. In this work we propose a multivariate bisection method supported by the Poincar'e-Miranda theorem in order to solve non-linear system of equations. Given an initial cube verifying the hypothesis of Poincar'e-Miranda theorem the algorithm performs congruent refinements throughout its center by generating a root approximation. Throughout preconditioning we will prove the local convergence of this new root finder methodology and moreover we will perform a numerical implementation for the two dimensional case.